The transposition reaction of bacteriophage Mu and the DNA integration reaction of HIV, as well as the structural organization and dynamics of the chromosomes that are the target of these mobile genetic elements are studied in this project. A pair of DNA cleavages and strand transfers involving the ends of Mu or HIV DNA sequence and a target DNA are critical reaction steps that generate branched DNA intermediates. The two chemical reaction steps take place within higher order protein-DNA complexes called transpososome (for Mu) or preintegration complex (for HIV), the core of which is composed of two end segments of the transposing donor DNA synapsed by a tetramer of MuA transposase or HIV IN protein. The assembly of these higher order protein-DNA complexes and the catalytic activities of the protein within the assembled complex are controlled by a variety of factors, not all of which are well understood. This project aims to advance our understanding of how the viral DNA integration processes are controlled by the structural components and their dynamic interactions within and among the complexes. The molecular interactions involved in the Mu transposition complex and HIV preintegration complex have been studied by using fluorescence labeled proteins and DNA substrates. Fluorescence-based tools have been developed for assaying Mu DNA end pairing, stable synaptic complex formation, and other reaction steps. This study led to better understanding of the organization of the Mu-end synaptic complex and also identification of a new reaction intermediate. HIV DNA within a preintegration complex is protected by BAF protein, which is believed to condense DNA in a way that makes it inaccessible for self-destructive auto-integration. The mechanism of DNA condensation by BAF has been studied at a single DNA-molecule level by using fluorescence labeled BAF and a high-sensitivity fluorescence microscope system. The kinetic properties of the protein-DNA interaction and DNA condensation have been investigated. The impacts of other DNA-condensing proteins, from both prokaryotic and eukaryotic origins in addition to BAF, on the structural dynamics of DNA are studied in this project by employing a variety of techniques.